First weed is common lambsquarters. 

At the bottom of the first pic, to the left of center, notice the small weed with the very long elliptical leaves.  This is Lambsquarters showing its cotyledon leaves.  It will grow to look like the larger plant above it. When you can identify lambsquarters in the cotyledon leaf stage, you are pretty good at weed ID.

I believe the second weed is Veronica Speedwell, or Common Speedwell.   I tend to call it Veronica, which is the Genus name.

This weed does not get very tall, but spreads out close to the ground.